Well‐balanced nonstaggered central schemes based on hydrostatic reconstruction for the shallow water equations with Coriolis forces and topography. (29th August 2020)

• Record Type: Journal Article
• Authors: Dong, Jian; Li, Ding Fang
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 2(2021)
• Page Start: 1358
• Page End: 1376
• Publication Date: 2020-08-29
• Subjects: Coriolis forces -- hydrostatic reconstruction -- nonstaggered central schemes -- positivity preserving -- Saint‐Venant systems -- well‐balancing; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6835
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The objective of this paper is to present a nonstaggered central scheme based on hydrostatic reconstruction (HR) for the shallow water equations with Coriolis forces and nonflat bottom topography. The discretization of the bed slope source term is based on the HR method to ensure the well‐balanced property for the stationary solution. We use the cell average of the discharge on the staggered cell to discretize the source term due to the effect of Coriolis forces. The positivity‐preserving property of the water depth is obtained by providing an appropriate CFL condition with the help of a "draining" time‐step technique. Finally, several two‐dimensional numerical results of classical problems of the system are presented to test these properties of the current scheme.